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Oscillation of second-order delay dynamic equations on time scales

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An Erratum to this article was published on 18 April 2012

Abstract

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations

$$\bigl(p(t)\bigl(x^{\Delta}(t)\bigr)^{\gamma}\bigr)^{\Delta}+q(t)f\bigl(x\bigl(\tau(t)\bigr)\bigr)=0$$

on a time scale \(\mathbb{T}\) , here γ≥1 is a quotient of odd positive integers with p and q real-valued positive rd-continuous functions defined on \(\mathbb{T}\) . Our results improve and extend some results established by Saker (J. Comput. Appl. Math. 177:375–387, 2005) but also unify the oscillation of the second order nonlinear delay differential equation and the second order nonlinear delay difference equation.

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Authors and Affiliations

  1. School of Science, University of Jinan, Jinan, Shandong, 250022, People’s Republic of China

    Shurong Sun & Zhenlai Han

  2. School of Control Science and Engineering, Shandong University, Jinan, Shandong, 250061, People’s Republic of China

    Zhenlai Han & Chenghui Zhang

Authors
  1. Shurong Sun
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  2. Zhenlai Han
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  3. Chenghui Zhang
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Corresponding author

Correspondence to Zhenlai Han.

Additional information

This research is supported by the Natural Science Foundation of China (60774004) and supported by Shandong Research Funds (Y2007A27), also supported by University of Jinan Research Funds for Doctors (B0621).

An erratum to this article can be found at http://dx.doi.org/10.1007/s12190-012-0563-y

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Sun, S., Han, Z. & Zhang, C. Oscillation of second-order delay dynamic equations on time scales. J. Appl. Math. Comput. 30, 459–468 (2009). https://doi.org/10.1007/s12190-008-0185-6

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  • DOI: https://doi.org/10.1007/s12190-008-0185-6

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